Chapter 5Chapter 5 GasesGases

List, Pass,Amass

What are some things you rememberabout gases and their behavior?

Elemental States at 25Elemental States at 25ooCCHe

Rn

XeI

KrBrSe

ArClS

NeFO

P

NC

H

Li

Na

Cs

Rb

K

TlHgAuHfLsBa

Fr

PtIrOsReWTa PoBiPb

Be

Mg

Sr

Ca

CdAgZrY PdRhRuTcMoNb

AcRa

ZnCuTiSc NiCoFeMnCrV

In SbSn

Ga Ge

Al

Gd

Cm

Tb

Bk

Sm

Pu

Eu

Am

Nd

U

Pm

Np

Ce

Th

Pr

Pa

Yb

No

Lu

Lr

Er

Fm

Tm

Md

Dy

Cf

Ho

Es

At

Te

As

Si

B

5 - 2

SolidLiquidGas

Stuff You Already KnowStuff You Already Know State

Property Solid Liquid Gas

Density

Shape

Compressibility

Thermalexpansion

High High Low

Fixed Takes shape Expands of lower part to fill the

of container container

Small Small Large

Very Small Moderate Small

More You RememberMore You RememberIn this state, the particles have sufficient

energy to overcome all forces that attract them to each other.

Each particle is completely separated from the others.

This results in low densities and the fact that gases completely fill the container that holds them.

Gas PressureGas PressureGases exhibit pressure on the containers

that hold them.

Pressure = Force / Area Units: N/m2 a.k.a. Pascal

760 mmHg = 1 atm = 760 torr = 1.01x105 Pa

Standard Pressures

Oneatm

760 mmHg

29.9 inHg

vacuum

Manometer measures air pressure of a gas in a contained system.

Barom

eter

mea

sure

s

ambien

t air

press

ure.

Boyles LawBoyles LawP1V1 = P2V2

Pressure and volume are inversely proportional.

Examine the graph of the data:Derivative!

Data!

Charles’ LawCharles’ Law V1/T1 = V2/T2

Volume and Temperature are directly proportional.

Check out data:

All gases intersect the x axis at a temperature of 0 Kelvin(-273 oC).

At temperatures lower than 0 Kelvin, gases would have a negative volume (impossible, as is negative Kelvin degrees)

Avogadro’s LawAvogadro’s LawP1/n1 = P2/n2

Guy-Lussac’s LawGuy-Lussac’s Law P1/T1 = P2/T2

Also, at constant pressure and temperature, the volumes of gases involved in a chemical reaction are related by small whole numbers.(ie: 2 “volumes” of hydrogen and 1 “volume” of oxygen combine to form 2 “volumes” of

water…we can use volume and moles similarly when it comes to gas stoichiometry.)

Ideal Gas LawIdeal Gas Law PV = nRT

R = 0.0821 Latm/Kmol

When you hold variables constant, this equation can be manipulated into one of the others that we just talked about.

Since ideal gases don’t exist, this equation expresses the behavior a real gas approaches as pressure is lowered and temperature is increased.

22

22

11

11

Tn

VPR

Tn

VP

Gas StoichiometryGas StoichiometryAt STP, the molar volume of a gas

is 22.4 L / mole

S.T.P.

Temperature = 273.15 K (0 oC)Pressure = 1 atm

Gas stoichiometry problems can involve a gas law and/or the molar volume of a gas.

Demo and ThoughtsDemo and Thoughts

What is inside the can?Why does this happen?Which gas law(s) does it

illustrate?

Rearrange the ideal gas law to get an equation to solve for the molar mass of a gas.

AnswerNow

Section 5.5:Section 5.5: Dalton’s Law of Partial PressureDalton’s Law of Partial Pressure

• For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert independently.

Ptotal= P1 + P2 + P3, etc…

Air is a mixture of gases:

Pair = PN2 + PO2

+ PAr + PCO2 + PH2O

Air is a mixture of gases:

Pair = PN2 + PO2

+ PAr + PCO2 + PH2O

The law of partial pressures also works for moles.

Ptotal= (n1 + n2 +…)(RT/V)

In a mixture of ideal gases, it is the TOTAL NUMBER OF MOLES OF PARTICLES, not the identity of the substance, that determines the pressure.

Partial Pressure Try MePartial Pressure Try MeMixtures of helium and oxygen are used in

scuba diving tanks to help prevent “the bends.”

For a particular dive, 46 liters of O2 and 12 liters of He were pumped in to a 5 liter tank. Both gases were added at 1.0 atm pressure at 25oC.

Determine the partial pressure for both gases in the scuba tank at 25oC. Then, determine the total pressure in the tank.

atmL

KmolP

atmL

KmolP

molK

Latmn

molK

Latmn

He

O

He

O

4.25

)15.298)(0821.0)(49.0(

3.95

)15.298)(0821.0)(9.1(

49.0)15.298)(0821.0(

)12)(0.1(

9.1)15.298)(0821.0(

)46)(0.1(

2

2

P total = P He + P O2

P total = 9.3 + 2.4

P total = 11.7 atm

Mole FractionsMole Fractions• Another way to determine the partial

pressures of a gas.

X = n1 = P1

ntotal Ptotal

Chi,mole

fraction

When Gas Is Collected Over WaterWhen Gas Is Collected Over Water

• You must include the partial pressure of water in your calculations.

• The vapor pressure of water is a constant value at each temperature. (you would need to look this up on a table or it would be given to you.)

At 22oC, PH2O is 21 torr

Section 5.6:Section 5.6: Effusion and DiffusionEffusion and DiffusionEffusion occurs

when a gas passes through a small opening in a barrier.

Diffusion occurs when two gases mix randomly and spontaneously.

More on Diffusion, Effusion, More on Diffusion, Effusion, and speed of moleculesand speed of molecules• The speed of diffusion is much less than the

theoretical velocity of the gas because of COLLISIONS.

• The average speed of a gas that is effusing is proportional to the averages speed squared.

MRTurms 3

R = 8.314 J/Kmol

Even more on velocity of molecules Even more on velocity of molecules that are effusing and/or diffusingthat are effusing and/or diffusing

• Graham’s Law: The rates of the gases is proportional to the square root of the inverse of the molar masses of the gases.

1

2

2

1

M

M

V

V

Kinetic Molecular TheoryKinetic Molecular Theory

• Kinetic Molecular Theory is an attempt to describe the behavior of an ideal gas

1. The particles are so tiny and spread out that their volume is negligible.

2. Particles in constant motion collisions w/ walls cause pressure.

3. Particles exert no intermolecular force.4. Average KE is directly proportional to

Kelvin temperature.

Can we explain each gas Can we explain each gas law using KMT?law using KMT?

• Boyle’s Law

• Gay-Lussac

• Charles

• Avogadro

KMT tutorialKMT tutorial

www.wwnorton.com/college/ chemistry/gilbert/tutorials/ch8.htm

Maxwell-Boltzman Maxwell-Boltzman Distribution CurvesDistribution Curves

• Seen in wwnorton tutorial.

• Illustrates the number of particles at a given velocity and temperature.

Gases are not PerfectGases are not Perfect• Particles DO have mass and

volume• Small attractive forces between

particles ARE sometimes significant

• Higher concentration of gas, more forces

• Under extreme pressures or at low temperature, gases will condense to liq./sol.

Ideal vs Real behaviorIdeal vs Real behavior

Nitrogen atVarious temp.

Various GasDeviations

Well, Now What?Well, Now What?The ideal gas law has to be adjusted

to reflect REAL gas behavior.

I DO!!!

Johannes van der Waals

…Yes, he’s the intermolecular force guy, and its no coincidence!

What Johannes Did…What Johannes Did…

nRTPV

)('

nbV

nRTP

2' )( VnaPPreal

1

3

2

5

42

)(

V

na

nbV

nRTPreal

nRTnbVxV

naPreal

)(

2

Ideal gas law

Adjusted for volume of gas

Adjusted for intermolecular forces

Glued Together

The Official Equation

When should you use When should you use vanderWaals equation?vanderWaals equation?

• Whenever you want to know the REAL behavior of the gas, not just the ideal, limiting value.

• Whenever you are working at low temperatures or high pressures

• Whenever you need to employ KMT to explain the behavior of a gas …AND BE CORRECT ALL THE TIME.

But how do you know the But how do you know the values of a and b?values of a and b?

• They are constants. You can look them up!

Show Me ProblemShow Me Problem

Calculate the pressure exerted by 0.500 mol of nitrogen in a 1.00L container at 25.0oC using

a) The Ideal Gas Lawb) The van der Waals Equation

a) The Ideal Gas Law Way

PV =nRTP(1.00) = (.500)(.0821)(298)

P = 12.2 atm

b) van der Waals Way

(Pobs+a(n/V)2)(V-nb)=nRT(Pobs+1.39(.500/1.00)2)(1.00-.500(.0391))=(0.500)(0.0821)(298)

(Pobs +5.56)(.98045)=12.23Pobs=(12.23/0.98045)-5.56 = 6.92 atm

Try Me ProblemTry Me Problem

Calculate the pressure exerted by 0.250 mol of argon in a 1.00L container at 23.0oC using

a) The Ideal Gas Lawb) The van der Waals Equation

Atmospheric ChemistryAtmospheric Chemistry• Air is a homogeneous mixture!

• The heavier gases exist in the lower atmosphere, while lighter gases are present in the upper atmosphere.

• Radon gas found in basements because it is very heavy.

• Oxygen is less prevalent at the tops of mountains.• Hydrogen is more prevalent as you gain altitude.

• Troposphere (closest to us) is most greatly impacted by our every-day routines.

N2 N2 Ar Ar H2

H2

Ne

Ne

O2 O2

CO2 CO2

He

He

Kr Kr

CH4CH4

NO

NO

H2

O

H2

O

Xe

Xe

Causes of Air Pollution and Causes of Air Pollution and Acid RainAcid Rain

Causes:-Generation of electricity

Coal burning plants-Transportation

Combustion of petroleum

Acid Rain Effects on Acid Rain Effects on BuildingsBuildings

• Erosion of the stone• Blackened streaks on

bricks

Why?Why?Limestone (calcium carbonate) reacts with

acid rain (sulfuric acid):

CaCO3 + H2SO4 CaSO4 + H2CO3

H2CO3 CO2 gas + H2O

Calcium sulfate is soluble in water, which means that the

limestone will wash away as the rain pours over it.

Chemistry of Acid Rain as Chemistry of Acid Rain as caused by burning coalcaused by burning coal

22 SOOS

322 22 SOOSO

4223 SOHOHSO

Prevention of Acid RainPrevention of Acid Rain

• At coal plants: Injection of limestone and

air into combustion chamber before products are allowed to escape.

(product becomes CaSO3, which is unusable, but non-toxic)

Air Pollution Effects on Air Pollution Effects on PeoplePeople

• Burning eyesBurning eyes• Trouble breathingTrouble breathing• HeadachesHeadaches• FatigueFatigue• Photochemical smogPhotochemical smog

Chemistry of Air Pollution as Chemistry of Air Pollution as caused by excessive trafficcaused by excessive traffic

NOON 22

2NONO

ONONO 2

32 OOO **

23 OOO

OHOHO 22*

32 HNONOOH